That question is an oxymoron. First it is a Tradition, not tradition, and secondly, the Schism of 1054 did not affect the Tadition, which lives in both particualr Catholic Churchs, East and West, both being One Holy Catholic and Apostolic Church. The fact that these two communities are not in communion is a different issue.
But since the big T traditions differ about, lets say Purgatory and the Authority of the RC pope; two of the initial causes of the Protestant break from the RC's. That shows within the 'Unified RC/OC church' there are infallible doctrines of the RC church that either are not infallible, showing their authority is wrong, or the big T traditions of the OC are wrong. Hence the Schism.
It cannot be unified if one side is big R Right and does not agree with the other on something it rests its authority over ALL the small C catholic church.
This talk of Tradition just seems, and it is not meant as an insult, but it seems to this interested observer, that the OC knows if the RC Traditions are questioned, that soon theirs will be also, since they come from the same roots and as 'inspired' traditions must logically be the same lest they are shown to not be. The reason they must reconcile, and cannot reconcile is because of these Traditions.
And the Reformed say that since they ain't the same they must not be, just as a Prophet must be right 100% of the time or he isn't inspired by God.
The only thing we have that we all agree is inspired are the 8000 translations of the apostles written word in the Koine, Hebrew and Aramaic.
(sorry if this is confused. Early morning without the bean-juice.)